Neural networks for solving linear inequality systems

In this paper a neural network approach to the on-line solution of linear inequality systems is considered. Three different techniques are discussed and for each technique a novel neural network implementation is proposed. The first technique is a standard penalty method implemented as an analog neural network. The second technique is based on the transformation of inequality constraints into equality constraints with simple bounds on the variables, The transformed problem is then solved using least squares (LS) and least absolute values (LAV) optimisation criteria. The third technique makes use of the regularised total least squares criterion (RTLS). For each technique a suitable neural network architecture and associated algorithm in the form of nonlinear differential equations has been developed. The validity and performance of the proposed algorithms has been verified by computer simulation experiments. The analog neural networks are deemed to be particularly well suited for high throughput, real time applications.